An exact minimization algorithm for generalized Reed-Muller expressions

A generalized Reed-Muller expression (GRM) is obtained by negating some of the literals in a positive polarity Reed-Muller expression (PPRM). There are at most 2/sup n2(n-1)/ different GRMs for an n-variable function. A minimum GRM is one with the fewest products. This paper presents certain propert...

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Veröffentlicht in:1994 IEEE Asia-Pacific Conference on Circuits and Systems S. 460 - 465
Hauptverfasser: Sasao, T., Dednath, D.
Format: Tagungsbericht
Sprache:Englisch
Japanisch
Veröffentlicht: IEEE 17.12.2002
Schlagworte:
Adders
Circuit testing
Computer science
Logic design
Logic functions
Logic testing
Minimization methods
ISBN:0780324404, 9780780324404
Online-Zugang:Volltext
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Abstract A generalized Reed-Muller expression (GRM) is obtained by negating some of the literals in a positive polarity Reed-Muller expression (PPRM). There are at most 2/sup n2(n-1)/ different GRMs for an n-variable function. A minimum GRM is one with the fewest products. This paper presents certain properties and an exact minimization algorithm for GRMs. The minimization algorithm uses binary decision diagrams. Up to five variables, all the representative functions of NP-equivalence classes were generated, and minimized. A table compares the number of products necessary to represent 5-variable functions for 7 classes of expressions: FPRMs, KROs, PSDRMs, PSD-KROs, GRMs, ESOPs, and SOPs. GRMs require, on the average, fewer products than sum-of-products expressions and have easily testable realizations.
AbstractList A generalized Reed-Muller expression (GRM) is obtained by negating some of the literals in a positive polarity Reed-Muller expression (PPRM). There are at most 2/sup n2(n-1)/ different GRMs for an n-variable function. A minimum GRM is one with the fewest products. This paper presents certain properties and an exact minimization algorithm for GRMs. The minimization algorithm uses binary decision diagrams. Up to five variables, all the representative functions of NP-equivalence classes were generated, and minimized. A table compares the number of products necessary to represent 5-variable functions for 7 classes of expressions: FPRMs, KROs, PSDRMs, PSD-KROs, GRMs, ESOPs, and SOPs. GRMs require, on the average, fewer products than sum-of-products expressions and have easily testable realizations.
Author Sasao, T.
Dednath, D.
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  surname: Dednath
  fullname: Dednath, D.
  organization: Dept. of Comput. Sci. & Electron., Kyushu Inst. of Technol., Iizuka, Japan
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Snippet A generalized Reed-Muller expression (GRM) is obtained by negating some of the literals in a positive polarity Reed-Muller expression (PPRM). There are at most...
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StartPage 460
SubjectTerms Adders
Circuit testing
Computer science
Logic design
Logic functions
Logic testing
Minimization methods
Title An exact minimization algorithm for generalized Reed-Muller expressions
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